There's no indication of a link in the biographical information for Sir James Dewar, of which this is perhaps the best online:
[ url needs to be updated ]
and the wikipedia entry is also useful:
Information about the origins of the company (John Dewar & Sons) who originally made the whisky is harder to come by, but that company was evidently founded in Perth whereas Sir James' family were innkeepers in Kincardine, near Stirling. Whilst it isn't impossible that there is a link, the two families seem not to be closely related. Dewar is not an especially uncommon name.